Performance analysis of least squares algorithm for multivariable stochastic systems

Ziming Wang; Yiming Xing; Xinghua Zhu

Kybernetika (2023)

  • Volume: 59, Issue: 1, page 28-44
  • ISSN: 0023-5954

Abstract

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In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.

How to cite

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Wang, Ziming, Xing, Yiming, and Zhu, Xinghua. "Performance analysis of least squares algorithm for multivariable stochastic systems." Kybernetika 59.1 (2023): 28-44. <http://eudml.org/doc/299061>.

@article{Wang2023,
abstract = {In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.},
author = {Wang, Ziming, Xing, Yiming, Zhu, Xinghua},
journal = {Kybernetika},
keywords = {least squares; martingale theory; non-persistent excitation},
language = {eng},
number = {1},
pages = {28-44},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Performance analysis of least squares algorithm for multivariable stochastic systems},
url = {http://eudml.org/doc/299061},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Wang, Ziming
AU - Xing, Yiming
AU - Zhu, Xinghua
TI - Performance analysis of least squares algorithm for multivariable stochastic systems
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 1
SP - 28
EP - 44
AB - In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.
LA - eng
KW - least squares; martingale theory; non-persistent excitation
UR - http://eudml.org/doc/299061
ER -

References

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